Estimate the minimum sample size needed to achieve the margin of error E = 0.029 for a 95% confidence intervail The minimum sample size is ... (Round up to the nearest integer.)

MATLAB: An Introduction with Applications
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**Estimating Minimum Sample Size for a Given Margin of Error**

To ensure the accuracy and reliability of statistical results, it is essential to determine the minimum sample size needed. This helps achieve the desired margin of error in research studies. Below is an example of how to calculate this for a specific scenario.

**Scenario:**

Objective: Estimate the minimum sample size needed to achieve a margin of error (E) of 0.029 for a 95% confidence interval.

**Instructions:**

1. **Determine the Margin of Error and Confidence Level:**
   - Margin of Error (E): 0.029
   - Confidence Level: 95%

2. **Calculate the Minimum Sample Size:**
   - The sample size can be determined using the formula for sample size calculation, which involves the standard deviation and critical value from the Z-distribution corresponding to the confidence level.

3. **Round Up to the Nearest Integer:**

   Ensure the calculated sample size is rounded up to the nearest whole number to guarantee sufficient sample size.

To answer the prompt, input the calculated sample size:

The minimum sample size is [ ]. *(Round up to the nearest integer.)*

This step is essential in statistical analysis, helping researchers avoid underestimating or overestimating the necessary sample size, leading to more accurate and reliable data interpretations.
Transcribed Image Text:**Estimating Minimum Sample Size for a Given Margin of Error** To ensure the accuracy and reliability of statistical results, it is essential to determine the minimum sample size needed. This helps achieve the desired margin of error in research studies. Below is an example of how to calculate this for a specific scenario. **Scenario:** Objective: Estimate the minimum sample size needed to achieve a margin of error (E) of 0.029 for a 95% confidence interval. **Instructions:** 1. **Determine the Margin of Error and Confidence Level:** - Margin of Error (E): 0.029 - Confidence Level: 95% 2. **Calculate the Minimum Sample Size:** - The sample size can be determined using the formula for sample size calculation, which involves the standard deviation and critical value from the Z-distribution corresponding to the confidence level. 3. **Round Up to the Nearest Integer:** Ensure the calculated sample size is rounded up to the nearest whole number to guarantee sufficient sample size. To answer the prompt, input the calculated sample size: The minimum sample size is [ ]. *(Round up to the nearest integer.)* This step is essential in statistical analysis, helping researchers avoid underestimating or overestimating the necessary sample size, leading to more accurate and reliable data interpretations.
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